Abstract
Abstract. The one-parameter division undistortion model by (Lenz, 1987) and (Fitzgibbon, 2001) is a simple radial distortion model with beneficial algebraic properties that allows to reason about some problems analytically that can only be handled numerically in other distortion models. One property of this distortion model is that straight lines in the undistorted image correspond to circles in the distorted image. These circles are fully described by their center point, as the radius can be calculated from the position of the center and the distortion parameter only. This publication collects the properties of this distortion model from several sources and reviews them. Moreover, we show in this publication that the space of this center is projectively isomorphic to the dual space of the undistorted image plane, i.e. its line space. Therefore, projective invariant measurements on the undistorted lines are possible by the according measurements on the centers of the distorted circles. As an example of application, we use this to find the metric distance of two parallel straight rails with known track gauge in a single uncalibrated camera image with significant radial distortion.
Highlights
A REVIEW OF THE ONE-PARAMETER DIVISION UNDISTORTION MODELBastian Erdnußa,b,∗ aInstitute of Photogrammetry and Remote Sensing (IPF), Karlsruhe Institute of Technology (KIT) bFraunhofer-IOSB (Institute of Optronics, System Technologies and Image Exploitation) KEY WORDS: Projective Invariance, Cross-Ratio, Radial Distortion, Division Model, Rails Distance
A main objective of photogrammetry is to obtain metric information about physical objects from images thereof
OpenCV (Bradski, 2000) uses a camera model with up to 18 parameters for camera calibration and Metashape (Agisoft LLC, 2021) uses still up to 12 parameters for the frame camera model. These models can lead to very accurate results for laboratory calibrations of measuring cameras or for auto-calibration during bundle adjustment in structure from motion applications, if sufficiently many well distributed feature correspondences in enough frames are available
Summary
Bastian Erdnußa,b,∗ aInstitute of Photogrammetry and Remote Sensing (IPF), Karlsruhe Institute of Technology (KIT) bFraunhofer-IOSB (Institute of Optronics, System Technologies and Image Exploitation) KEY WORDS: Projective Invariance, Cross-Ratio, Radial Distortion, Division Model, Rails Distance.
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